Let the movie star's current age be $x$ and his daughter's current age be $y$.

Step 1: Set up the equations

1. Seven years ago:

   • The star's age was $x - 7$.
   • His daughter's age was $y - 7$.
   • At that time, the star says, "I was eleven times as old as my daughter": $x - 7 = 11(y - 7)$

2. Now:

   • The star says, "I am four times as old as my daughter": $x = 4y$

Step 2: Solve the system of equations

Equation 1:

$x - 7 = 11(y - 7)$ Expand the right-hand side: $x - 7 = 11y - 77$ Simplify: $x = 11y - 70 \quad \text{(Equation A)}$

Equation 2:

$x = 4y \quad \text{(Equation B)}$

Step 3: Substitute Equation B into Equation A

Substitute $x = 4y$ from Equation B into Equation A: $4y = 11y - 70$ Simplify: $70 = 11y - 4y$ $70 = 7y$ $y = 10$

Step 4: Solve for $x$

Substitute $y = 10$ into Equation B: $x = 4y = 4(10) = 40$

Conclusion

The movie star is 40 years old.

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Would you like more details or have any questions?

Here are five related questions to explore further:

1. How old was the star seven years ago?
2. How old is the star's daughter now?
3. How old was the daughter seven years ago?
4. How do we solve the system of equations using substitution and elimination?
5. What would happen if the age ratio seven years ago was different?

Tip: When solving word problems, clearly define variables for unknown quantities and set up equations based on the relationships described.